波特图 极点和零点

2019-04-10

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零点：当系统输入幅度不为零且输入频率使系统输出为零时，此输入频率值即为零点。

极点：当系统输入幅度不为零且输入频率使系统输出为无穷大（系统稳定破坏，发生振荡）时，此频率值即为极点。

每一个极点之处，增益衰减-3db，并移相-45度。极点之后每十倍频，增益下降20db.

零点与极点相反;每一个零点之处，增益增加3db，并移相45度。零点之后，每十倍频，增益增加20db。

极点

极点增益和相位

Pole Location = fP (cutoff freq)
Magnitude (f < fP) = GDC (for example, 100 dB)
Magnitude (f = fP) = –3 dB
Magnitude (f > fP) = –20 dB/decade
Phase (f = –45°)
Phase (0.1 fP < f < 10 fP) = –45°/decade
Phase (f > 10 fP) = –90°
Phase (f < 0.1 fP) = 0°

极点公式

Gv = voltage gain in V/V
GdB = voltage gain in decibels
GDC = the dc or low frequency voltage gain
f = frequency in Hz
fP = frequency at which the pole occurs
θ = phase shift of the signal from input to output
j = indicates imaginary number or √ –1

零点

零点增益和相位

Zero location = fZ
Magnitude (f < fZ) = 0 dB
Magnitude (f = fZ) = +3 dB
Magnitude (f > fZ) = +20 dB/decade
Phase (f = fZ) = +45°
Phase (0.1 fZ < f < 10 fZ) = +45°/decade
Phase (f > 10 fZ) = +90°
Phase (f < 0.1 fZ) = 0°

零点公式

GV = voltage gain in V/V
GdB = voltage gain in decibels
GDC = the dc or low frequency voltage gain
f = frequency in Hz
fZ = frequency at which the zero occurs
θ = phase shift of the signal from input to output
j = indicates imaginary number or √ –1